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Answer :
To evaluate the polynomial [tex]\( 7x^3 + 6x^6 - 8 \)[/tex] at a specific value of [tex]\( x \)[/tex], let’s break it down step-by-step. We'll assume [tex]\( x = 2 \)[/tex].
1. Calculate [tex]\( x^3 \)[/tex]:
[tex]\( 2^3 = 8 \)[/tex].
2. Calculate the term [tex]\( 7x^3 \)[/tex]:
Multiply [tex]\( 7 \)[/tex] by [tex]\( 8 \)[/tex] (which is [tex]\( 2^3 \)[/tex]):
[tex]\( 7 \times 8 = 56 \)[/tex].
3. Calculate [tex]\( x^6 \)[/tex]:
[tex]\( 2^6 = 64 \)[/tex].
4. Calculate the term [tex]\( 6x^6 \)[/tex]:
Multiply [tex]\( 6 \)[/tex] by [tex]\( 64 \)[/tex] (which is [tex]\( 2^6 \)[/tex]):
[tex]\( 6 \times 64 = 384 \)[/tex].
5. Combine all the terms to evaluate the polynomial:
Add the results together and then subtract 8:
[tex]\( (56 + 384) - 8 = 440 - 8 = 432 \)[/tex].
So, the value of the polynomial [tex]\( 7x^3 + 6x^6 - 8 \)[/tex] when [tex]\( x = 2 \)[/tex] is 432.
1. Calculate [tex]\( x^3 \)[/tex]:
[tex]\( 2^3 = 8 \)[/tex].
2. Calculate the term [tex]\( 7x^3 \)[/tex]:
Multiply [tex]\( 7 \)[/tex] by [tex]\( 8 \)[/tex] (which is [tex]\( 2^3 \)[/tex]):
[tex]\( 7 \times 8 = 56 \)[/tex].
3. Calculate [tex]\( x^6 \)[/tex]:
[tex]\( 2^6 = 64 \)[/tex].
4. Calculate the term [tex]\( 6x^6 \)[/tex]:
Multiply [tex]\( 6 \)[/tex] by [tex]\( 64 \)[/tex] (which is [tex]\( 2^6 \)[/tex]):
[tex]\( 6 \times 64 = 384 \)[/tex].
5. Combine all the terms to evaluate the polynomial:
Add the results together and then subtract 8:
[tex]\( (56 + 384) - 8 = 440 - 8 = 432 \)[/tex].
So, the value of the polynomial [tex]\( 7x^3 + 6x^6 - 8 \)[/tex] when [tex]\( x = 2 \)[/tex] is 432.
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